equidistance in relation to two points

A collection of points is given in a pile to the left. Drag the points so that each point is equidistant to A and B. Distribute the points so that they, as a collection, are spanning across a wide region.
Discuss any and all observations you have with your group.
Now click a couple of the boxes to the right that are labeled with pairs of segments to help visualize the distances from each point that you dragged to A and B.
Unclick the boxes you clicked.
Now, click the boxes for line GE and segment AB. Discuss any observations you have with your group.
Can you pose a conjecture about the relationship between the dragged points and the static points A and B?